Temperature difference within catalyst pellet

Maintenance of isothermal conditions requires special care. Temperature differences should be minimised and heat-transfer coefficients and surface areas maximized. Electric heaters, steam jackets, or molten salt baths are often used for such purposes. Separate heating or cooling circuits and controls are used with inlet and oudet lines to minimize end effects. Pressure or thermal transients can result in longer Hved transients in the individual catalyst pellets, because concentration and temperature gradients within catalyst pores adjust slowly. 

Catalyst supports such as silica and alumina have low thermal conductivities so that temperature gradients within catalyst particles are likely in all but the finely ground powders used for infrinsic kinetic studies. There may also be a film resisfance fo heaf fransfer af fhe exfemal surface of the catalyst. Thus the internal temperatures in a catalyst pellet may be substantially different than the bulk gas temperature. The definition of the effectiveness factor, Equation 10.23, is unchanged, but an exothermic reaction can have reaction rates inside the pellet that are higher than would be predicted using the bulk gas temperature. In the absence of a diffusion limitation, rj > 1 would be expected for an exothermic reaction. (The case > 1 is also possible for some isothermal reactions with weird kinetics.) Mass transfer limitations may have a larger... 

Heat and mass transfer processes always proceed with finite rates. Thus, even when operating under steady state conditions, more or less pronounced concentration and temperature profiles may exist across the phase boundary and within the porous catalyst pellet as well (Fig. 2). As a consequence, the observable reaction rate may differ substantially from the intrinsic rate of the chemical transformation under bulk fluid phase conditions. Moreover, the transport of heat or mass inside the porous catalyst pellet and across the external boundary layer is governed by mechanisms other than the chemical reaction, a fact that suggests a change in the dependence of the effective rate on the operating conditions (i.e concentration and temperature). 

When comparisons between global and intrinsic rates are made, it is understood that the comparison is for the same temperature and concentration. Note that in a reactor operating at steady state the two rates are always the same, but the temperature and composition in the bulk fluid (i.e., the global conditions) are different from those at a site within the catalyst pellet. -For porous pellets with uniform distribution of catalytic material. If the catalyst is deposited only on the outer layer of the pellet, this is not true. 

As discussed in chapter 5, diffusion through catalyst pores represents a resistance to mass and heat transfer, which gives rise to concentration and temperature gradients within the catalyst pellet. This causes the rate of reaction in the solid phase to be different from that if the bulk phase conditions prevail inside the particle, and the rate of reaction should be integrated along the radius of the pellet to get the actual rate of reaction. 

Consider the packed-bed tubular reactor whose schematic diagram is shown in Figure P4.ll. It is a hollow eylindrical tube of uniform cross-sectional area A, packed with solid catalyst pellets, in which the exothermic reaction A Bis taking place. The packing is such that the ratio of void space to the total reactor volume— the void fraction—is known let its value be represented by E. The reactant flows in at one end at constant velocity v, and the reaetion takes place within the reactor. Obtain a theoretical model that will represent the variation in the reactant concentration C and reactor temperature r as a function of time and spatial position z. Consider that the temperature on the surface of the catalyst pellets Tg is different from the temperature of the reacting fluid and that its variation with time and position is also to be modeled. 

Figure 6.17.12 shows snapshots of the calculated concentration profiles inside a single pellet at three different modified residence times (corresponding to the gray symbols in Figure 6.17.11). For the calculation, a temperature of 200°C was chosen as an example for a strong limitation by pore diffusion, and thus the equilibrium concentrations are reached within a small distance from the external particle surface. The corresponding concentration gradients of all three isomers at the surface of the catalyst are also indicated. These gradients are needed as boundary conditions to solve the differential Eq. (6.17.11) for every time step.

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